Various methods and systems have been proposed to measure the location of a radiation source in three-dimensional space. By using one or two-dimensional measurements of the location of a source of radiation, typically measurements that have been made from multiple positions, the location of the light source in the space can be determined by calculation. One such method employs multiple angle-measuring optical sensors, each of which measures the location of the light source with respect to one of several angular dimensions. With the multiple sensors situated within a three dimensional coordinate system at known locations and orientations with respect to the coordinate system, the 3-dimensional (3-D) coordinates of the light source can be computed relative to that coordinate system. In these determinations, the light sources are assumed to be tiny with respect to the size of the volume in which they are located. They therefore have been considered to be point sources that radiate light outward over a relatively wide solid angle. In actuality, there is no such thing as a literal point source of light or other radiation. However, for mensuration purposes described herein, a very small light source in a relatively large volume of space is an adequate approximation. For brevity, these approximate point sources of radiation will hereinafter be referred to simply as point sources of radiation or light.
Many 3-D methods and systems have been described in previous literature and some have even been used in practice to determine the location of a point source of light in a three dimensional volume. Examples of such prior art are found in the following references:
H. Fuchs, J. Duran, B. Johnson, and Zvi. M. Kedem; "ACQUISITION AND MODELING OF HUMAN BODY FORM DATA", Proc. SPIE, v. 166, 1978, p 94-102. PA0 Jean-Claude Reymond, Jean-Luc Hidalgo; "SYSTEM FOR MONITORING THE MOVEMENTS OF ONE OR MORE POINT SOURCES OF LUMINOUS RADIATION", U.S. Pat. No. 4,209,254, Jun. 24, 1980. PA0 Y. Yamashita, N. Suzuki, M. Oshima; "THREE-DIMENSIONAL STEREOMETRIC MEASUREMENT SYSTEM USING OPTICAL SCANNERS, CYLINDRICAL LENSES, AND LINE SENSORS", Proc. SPIE, v. 361, 1983, p. 67-73. PA0 F. Mesqui, F. Kaeser, and P. Fischer; "REAL-TIME, NON-INVASIVE RECORDING AND 3-D DISPLAY OF THE FUNCTIONAL MOVEMENTS OF AN ARBITRARY MANDIBLE POINT", SPIE Biostereometrics 602, 1985, p 77-84. PA0 Sharon S. Welch, Kevin J. Shelton, and James I. Clemmons; "OPTICAL POSITION MEASUREMENT FOR A LARGE GAP MAGNETIC SUSPENSION SYSTEM", Proc. of the 37th International Instrumentation Symposium, San Diego, May 5-9, 1991, p. 163-182. PA0 Waldean A. Schulz; "METHOD AND APPARATUS FOR THREE-DIMENSIONAL NON-CONTACT SHAPE SENSING", U.S. Pat. No. 5,198,877, Mar. 30, 1993. PA0 Farhad Daghighian; "OPTICAL POSITION SENSING WITH DUOLATERAL PHOTOEFFECT DIODES", Sensors, 1994 November p. 31-39. PA0 Robert P. Burton and Ivan E. Sutherland; "TWINKLE BOX A THREE-DIMENSIONAL COMPUTER INPUT DEVICE", AFIPS Conference Proceedings 43, 1974, Chicago, Ill. PA0 Kevin Byard; "SYNTHESIS OF BINARY ARRAYS WITH PERFECT CORRELATION PROPERTIES CODED APERTURE IMAGING", Nuclear Instruments and Methods in Physics Research A336, 1993, p. 262-268. PA0 Kevin Byard; "AN OPTIMISED CODED APERTURE IMAGING SYSTEM", Nuclear Instruments and Method in Physics Research A313, 1992, p. 283-289. PA0 Walter C Chiou and Richard C Augeri; "SQUARE ANTI-SYMMETRIC UNIFORMLY REDUNDANT ARRAY CODED APERTURE IMAGING SYSTEM", U.S. Pat. No. 5,606,165, Feb. 25, 1997. PA0 E. E. Fenimore; "CODED APERTURE IMAGING: PREDICTED PERFORMANCE OF UNIFORMLY REDUNDANT ARRAYS", Applied Optics 17, 22, 1978, p. 3562-3570. PA0 E. E. Fenimore and T. M. Cannon; "CODED APERTURE IMAGING WITH UNIFORMLY REDUNDANT ARRAYS, Applied Optics 17.3, Feb. 1, 1978, p. 337-347. PA0 Ronald J. Geluk; "SYNTHETIC APERTURE SCANNER FOR DECODING A CODE IMAGE PRODUCED BY PENETRATING RADIATION, SUCH AS X-RAYS", U.S. Pat. No. 4,191,890, Mar. 4, 1980. PA0 Stephen R. Gottesman and Edward J. Schneid; "PSEUDO-NOISE PRODUCT CODED APERTURE ARRAYS AND METHOD FOR DESIGNING SAME", U.S. Pat. No. 5,036,546, Jul. 30, 1991. PA0 S. R. Gottesman and E. J. Schneid; "PNP--A NEW CLASS OF CODED APERTURE ARRAYS", IEEE Transactions on Nuclear Science 33.1, 1986 February, p. 745-749. PA0 Philippe Laudet and Jean-Pierre Roques; "RESOLUTION OF STRONG SOURCES FOR A GAMMA-RAY TELESCOPE USING CODED APERTURE IMAGING", Applied Optics 27:20, Oct. 15, 1988 p. 4226-4230. PA0 Masaru Matsuoka and Yoshili Kohmura; "A NEW CONCEPT OF X-RAY MICROSCOPES WITH A CODED APERTURE IMAGING MASK", Jpn. J. Appl. Phys. 34Jpn. J. Appl. Phys. 34:1:1, p. 372-373. PA0 Jean in 't Zand; "CODED APERTURE CAMERA IMAGING CONCEPT", Internet WWW site http://lheawww.gsfc.nasa.gov/docs/cai/coded.sub.-- intr.html, Oct. 7, 1997.
The complete disclosures of the above H. Fuchs, Sharon S. Welch, and Robert P. Burton references are incorporated herein by reference.
Such systems typically include multiple angular location sensors. Furthermore, each angular location sensor typically includes a linear position detector, such as photo-electric position sensitive detector (PSD), a linear photodiode array, or a linear charge-coupled device (CCD). The linear position detector may be a photosensitive semiconductor strip (in the case of a PSD) or a row of many discrete photosensitive elements called pixels (in the case of a CCD or photodiode array). Area (or two-dimensional) position detectors may also be used, but the present invention is particularly useful for linear (or one-dimensional) photodiode arrays or CCDs, which detect an image. The determination of a point in space using a two dimensional detector can be considered similar to determining that position by means of two linear position detectors that are disposed at right angles to each other. Therefore, the following description will concentrate on a single linear imaging detector that uses discrete pixels. It should be noted that, while a linear detector measures only one angle (for example elevation) to the point source of radiation, an area detector measures two angles (for example, elevation and azimuth) simultaneously. However, two linear image detectors require only 2N pixels, while an area image detector has N.multidot.N' pixels, where N is the number of pixel rows and N' is the number of pixel columns. Since N and N' usually exceed 500, the area detector requires the readout, storage, and processing of at least several hundred times as many pixels.
Each angular sensor also includes an optical system to focus the radiation from the point source into a narrow lineal real image, and to cause that image to cross the linear image detector at an approximately right angle. In reference to FIG. 1 (prior art), a cylindrical lens 27 is typically employed to focus light rays 15 from a point source 10 into a linear real image 31 that crosses the photosensitive strip 16 of the linear image detector 14 at approximately a right angle.
Standard spherical lens systems in general cannot be used with a one-dimensional angular sensor for this purpose, because the focused real image of a point source 10 produced by a spherical lens is a tiny spot of light. Because this image is a spot, rather than a line, in most cases it will focus off the photosensitive strip, that is, far to one side of it. This is because, although the linear detector's row of photosensitive pixels is long, it is only a few microns wide. Therefore, a cylindrical lens 27, rather than a spherical lens, has generally been used in such optical sensors to focus the point light source 10 into a line image 31. Some tiny portion of this line image intersects the linear row of pixels at approximately a right angle no matter where the point source is located in a relative large volume. A compound cylindrical lens, consisting of several individual positive or negative focal length lenses, has sometimes been used to mitigate optical problems. However, for simplicity only a single simple cylindrical lens 27 is illustrated in FIG. 1.
As shown in FIG. 2, a simple narrow aperture or slit 22 may be employed instead of employing a cylindrical lens to produce the linear real image, in the same way that a pinhole can replace a spherical lens in a conventional camera. A single, straight, precision slit 22 focuses light from a point source 10 onto a line image 32 that approaches a perfect line image. Such a slit might be a long, very narrow rectangular aperture within an opaque mask, for example. Furthermore, unlike the cylindrical lens shown in FIG. 1, the slit 22 has an infinite depth of field. That is, except for diffraction effects, the line image 32 is in sharp focus regardless of the distance of the point source 10 relative to the linear detector. Furthermore, the image will be as straight as the slit is, and present day technology can inexpensively manufacture masks with very precise optical apertures. So, as the light source moves along a path 12 parallel to the longitudinal axis of the slit, the point of intersection of the line image 32 and the photosensitive strip 16 remains constant. Furthermore, the image remains sharp regardless of the distance (range) of light source 10 from the slit 22. Further, the angular field of view may be easily changed by varying the distance between the slit 22 and the photosensitive strip 16. As the distance decreases, the field of view increases. These are significant advantages over lens based optics.
Unfortunately, one significant drawback to the slit 22 is its limited light gathering ability. This limitation produces a dim line image 32 in comparison to the image 31 produced by a typical cylindrical lens 27. This limitation restricts the range at which any practical sensor can detect the point light source 10, because, as is well known, the amount of incident light decreases inversely with square of the increasing distance. Even at shorter ranges, where the brightness of the image is sufficient for measurement, the light focused from a single slit still presents a poor signal-to-noise ratio (SNR), which limits the reliability of the measurement. Alternatively, a knife-edge (in effect, a "one-sided slit") or a very wide slit may be substituted for the slit 22. These options generally are worse than a narrow slit, because they flood the photosensitive detector with more ambient light, which competes with the real image of the point source while providing no additional substantive position information.
A second significant drawback to the slit 22 is its susceptibility to dust, imperfections, and smudges. For example, an opaque particle within the slit but near one edge may cause a shift in the centroid of the image when the shadow of the particle falls on the linear photosensitive detector. While there are ways to detect when this problem arises, it is undesirable and affects accuracy.
In reference to both FIGS. 1 and 2, note that a typical cylindrical lens 27 is more efficient than a slit 22 in concentrating the light that passes through it and is focused onto a small area on the photosensitive row of pixels 16. This is because the lens is considerably wider, and more light enters the lens 27 than the slit 22. Yet this light is concentrated onto roughly the same area as the image formed by the slit. That is one major advantage of using a lens. Another advantage is that the lens 27 is substantially immune to the effects of a moderate amount of dust on it, unlike a single slit aperture 22.
However, the cylindrical lens 27 has at least three major drawbacks. First, the linear real image 31 that is formed by a cylindrical lens is not an ideal straight line at all. As the light source moves along a path 12 parallel to the longitudinal axis of the lens, the point of intersection of the line image 31 on the photosensitive strip 16 moves a small distance. This adversely affects the accuracy of the determination of the location of the point light source. Second, for a fixed-focus arrangement of a cylindrical lens, the point where the line image 31 meets the photosensitive strip does not maintain a sharp focus as the point source 10 moves away from the optical centerline 11. This is especially true as the distance 12 increases, because a standard cylindrical lens presents a less circular and more elliptical curvature to those light rays 15 entering the lens from an angle that is far removed from the optical centerline of the camera. The result is an aberated real image 31 which is in poor focus. As the image becomes blurred, the location of the centroid of image is determined with less certainty (especially for a CCD with pixels that individually have diminished intensity). A third disadvantage of the lens 21 is that the sharpness of focus will be affected by the distance of point source 10 from the lens 21, especially for wider lenses that collect more light. This is the same depth-of-field effect as for standard spherical lenses with larger apertures.
These disadvantages limit the accuracy of measurement. Multiple lenses and light stops can improve the image characteristics, but such improvements are more costly, involve more difficult manufacturing, and still do not solve the problems well enough for high accuracy measurement. The nonlinear distortion can be modeled and corrected in the computation that calculates the three-dimensional location of the light source from the angle measurements provided by the multiple sensors. However, this correction is complex and in practice resorts to approximations. This is because the lens distortion correction for any one sensor cannot be made using only the data from itself alone. The correction depends on knowing both the azimuth and elevation angles of incidence of the light with respect to the cylindrical lens, but each sensor measures only one angle with respect to its own lens axis. While a slit as a replacement for the cylindrical lens does avoid the above problems, its limited light gathering ability, limited range, and its susceptibility to dust, smudges, and imperfections are major drawbacks. Therefore, there is a need for an optical system that captures the advantages of both slits and cylindrical lenses while it avoids their disadvantages.
Multiple apertures have been used in the prior art, but for different purposes than those of the instant invention. In the prior art, coded apertures (a patterned form of multiple apertures) have been used exclusively with area arrays, such as in connection with the area CCDs that are used in video cameras. The application of such coded apertures has previously been oriented toward the capture and reconstruction of complex two-dimensional images for visualization purposes. They have not been used to improve the precision of one dimensional sub-pixel location measurements. Historically, coded apertures have been used to collect more of the available radiation in X-ray imaging, because weaker sources of radiation are desirable from the patient's health perspective, and because conventional lenses cannot be used to focus X-rays. Coded apertures have also been used in connection with two-dimensional astronomical imaging, in which the sources of light are extremely dim. In the prior art, the apertures that were used for these purposes were usually plural pinholes arranged in a pseudo-random, two-dimensional array.
The following references are cited as examples of the state of the prior art being referred to above:
Included in some of the above references is the description of a particular form of coded aperture called a uniformly redundant array (URA). While the references employ two-dimensional URAs for imaging purposes, the present invention uses one-dimensional URAs specifically for angular position sensors. URAs have particular properties, which improve the results of applying a mathematical correlation to the image in order to determine its exact location. Unlike many arbitrary aperture patterns, which may generate multiple local peaks in the correlation, URAs generate a single, clear-cut peak, which corresponds directly to the location (displacement) of the image on the image detector.